A completely random alphanumeric password of length 16 has an entropy of 95 bits (16log2(226+10)). I forgot the exact value, but I think rar uses around 100k iterations for its KDF, increasing the security level by about 17 bits, resulting in an effective security level of 112 bits.
With standard GPUs breaking this would cost around $1019. Custom hardware shaves off a factor 100 or so, still giving you a cost of $1017. Even if Moore's law continues, it'll take several decades until this is remotely feasible.
Related question: How expensive is it to guess a 15 character password, and should I be worried?How expensive is it to guess a 15 character password, and should I be worried?
